Theorems · Theorem · real analysis
deriv_fun_const_smul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {R : Type u_2} [inst_3 : Monoid R] [inst_4 : DistribMulAction R F]
[SMulCommClass 𝕜 R F] [ContinuousConstSMul R F] (c : R),
DifferentiableAt 𝕜 f x → deriv (fun y => c • f y) x = c • deriv f x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Monoidstatement and proof · cited by 3,887
- SMulCommClassstatement and proof · cited by 1,927
- ContinuousConstSMulstatement and proof · cited by 832
- derivstatement · cited by 676
- DifferentiableAtstatement and proof · cited by 617
- DistribMulActionstatement and proof · cited by 584
- HasDerivAt.derivproof · cited by 147
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.const_smulproof · cited by 7
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